C₃²×D₇₇ #13063468

order	1386
isoclinism	isoclinic class of D₇₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×D₇₇
unambiguous semidirect product	C₁₁⋊(C₃²×D₇)

	subgroup	G/H
center, hypercenter	C₃²	D₇₇
commutator, cosocle, hypocenter	C₇×C₁₁	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁	C₂
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₃²

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 693

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3)(7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24);(4,5,6)(8,13)(9,12)(10,11)(15,24)(16,23)(17,22)(18,21)(19,20)

360 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1386, 23);